Climate-CH₄ feedback from wetlands and its interaction with the climate-CO₂ feedback

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with the climate-CO2 feedback

Bruno Ringeval, P. Friedlingstein, C. Koven, P. Ciais, N. de Noblet-Ducoudré, B. Decharme, P. Cadule

To cite this version:

Bruno Ringeval, P. Friedlingstein, C. Koven, P. Ciais, N. de Noblet-Ducoudré, et al.. Climate-CH4

feedback from wetlands and its interaction with the climate-CO2 feedback. Biogeosciences, European

Geosciences Union, 2011, 8 (8), pp.2137-2157. �10.5194/bg-8-2137-2011�. �hal-01806765�

www.biogeosciences.net/8/2137/2011/

doi:10.5194/bg-8-2137-2011

© Author(s) 2011. CC Attribution 3.0 License.

Biogeosciences

Climate-CH ₄ feedback from wetlands and its interaction with the climate-CO ₂ feedback

B. Ringeval

, P. Friedlingstein

, C. Koven

, P. Ciais

, N. de Noblet-Ducoudr´e

, B. Decharme

, and P. Cadule

1

Laboratoire des Sciences du Climat et de l’Environnement, UMR8212 – CEA-CNRS-UVSQ, CEA-Saclay, 91191 Gif-sur-Yvette, France

2

College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, EX44QF, UK

3

Lawrence Berkeley National Lab, 1 Cyclotron Rd., Berkeley, CA, USA

4

M´et´eo-France, CNRM/GMGEC/UDC, 31000 Toulouse, France

Received: 25 February 2011 – Published in Biogeosciences Discuss.: 23 March 2011 Revised: 18 July 2011 – Accepted: 31 July 2011 – Published: 9 August 2011

Abstract. The existence of a feedback between climate and methane (CH

) emissions from wetlands has previously been hypothesized, but both its sign and amplitude remain unknown. Moreover, this feedback could interact with the climate-CO

cycle feedback, which has not yet been ac- counted for at the global scale. These interactions relate to (i) the effect of atmospheric CO

on methanogenic substrates by virtue of its fertilizing effect on plant productivity and (ii) the fact that a climate perturbation due to CO

(respectively CH

) radiative forcing has an effect on wetland CH

emis- sions (respectively CO

fluxes at the surface/atmosphere in- terface).

We present a theoretical analysis of these interactions, which makes it possible to express the magnitude of the feed- back for CO

and CH

alone, the additional gain due to inter- actions between these two feedbacks and the effects of these feedbacks on the difference in atmospheric CH

and CO

be- tween 2100 and pre-industrial time (respectively 1CH

and 1CO

). These gains are expressed as functions of different sensitivity terms, which we estimate based on prior studies and from experiments performed with the global terrestrial vegetation model ORCHIDEE.

Despite high uncertainties on the sensitivity of wetland CH

emissions to climate, we found that the absolute value of the gain of the climate-CH

feedback from wetlands is relatively low (<30 % of climate-CO

feedback gain), with either negative or positive sign within the range of estimates.

Correspondence to: B. Ringeval (bruno.ringeval@lsce.ipsl.fr)

Whereas the interactions between the two feedbacks have low influence on 1CO

, the 1CH

could increase by 475 to 1400 ppb based on the sign of the C-CH

feedback gain.

Our study suggests that it is necessary to better constrain the evolution of wetland area under future climate change as well as the local coupling through methanogenesis substrate of the carbon and CH

cycles – in particular the magnitude of the CO

fertilization effect on the wetland CH

emissions – as these are the dominant sources of uncertainty in our model.

1 Introduction

Increased atmospheric CO

due to anthropogenic emissions is expected to lead to significant climate change in the 21st century (IPCC, 2007). Such climate change may indi- rectly affect the atmospheric CO

concentration by modify- ing the exchange of carbon between the atmosphere and the land and ocean. Several models have evaluated this climate- carbon cycle interaction, generally finding a positive feed- back between climate change and the global carbon cycle (Friedlingstein et al., 2006). Methane (CH

) is a very effi- cient greenhouse gas, with a Global Warming Potential of 25 (for given time horizon to 100 years) (IPCC, 2007), and is currently the second anthropogenic greenhouse gas after CO

. Very few studies have investigated the potential feed- back between CH

emissions by wetlands and climate.

CH

emissions from wetlands, the largest natural source

in the present-day global CH

budget, are directly controlled

by climatic conditions (e.g. Christensen et al., 2003). CH

emissions from wetlands depend on the global areal extent of wetlands (Ringeval et al., 2010; Bloom et al., 2010) and on the emission rate of these wetlands (e.g. Conrad, 1989;

Fung et al., 1991). Both of these terms are controlled by, among other variables, soil temperature and hydrology. For instance, temperature controls the rate of methanogenesis, exerts a control on the quality and quantity of organic ma- terial substrate for CH

production and has an influence on the area of wetlands through control of surface evaporation and the soil water budget. There is a large uncertainty in current global wetland emissions (estimates range from 115;

Fung et al., 1991 up to 237 TgCH

yr

; Hein et al., 1997).

Because the sensitivity of wetland CH

emissions to the en- vironmental control factors is poorly understood, the behav- ior of wetland CH

emissions under future climate change (e.g. Updegraff et al., 2001) and the amplitude of the result- ing climate-CH

emission feedback is far from being well understood.

Several studies have estimated changes in CH

emissions from wetlands under future climate change: e.g. Shindell et al. (2004) (hereinafter SWF04), Gedney et al. (2004) (hereinafter GCH04), Eliseev et al. (2008) (EMA08) and Volodin (2008) (V08). They all found an increase in CH

emissions despite differences in processes accounted for.

GCH04 and EMA08 also estimated the resulting climate- CH

feedback and both found it to be relatively small.

The additional warming induced by this feedback is small (e.g. only 3.7–4.9 % of the total projected warming by 2100 under the IS92a scenario found by GCH04). SWF04 ac- counts for changes in wetland area, using thresholds for variables they define as influencing wetland CH

emissions while GCH04 use a more realistic approach using a subgrid topographical model. EMA08 and V08 do not account for change in wetland extent. In these approaches, base CH

emissions are calculated using an empirical approach: pa- rameterization for GCH04 and EMA08 and correlations be- tween climate anomalies and wetland CH

emissions derived under current conditions for SWF04. With the exception of V08, none of these studies account for increasing CO

and its effect on plant productivity and hence on soil carbon avail- able for methanogenesis. Similarly, they do not account for the climate change (driven by CO

or CH

) effect on soil car- bon dynamics and hence on CH

emission rates. The strat- egy used by V08 is based on a more process-based approach which could allow accounting for these two effects but the contribution of each driver is not discussed.

In fact there is a tight coupling between the climate-CO

feedback and the climate-CH

feedback. As mentioned be- fore, increasing atmospheric CO

has a direct concentration effect on wetland CH

emissions. Moreover, CO

-induced climate change will affect CH

emissions, and hence CH

concentration and climate. CH

-induced climate change will in turn affect the land and ocean CO

cycle and hence at- mospheric CO

and climate. The combined effect of these two feedbacks (climate-CO

and climate-CH

) needs to be

explicitly accounted for in order to estimate the overall re- sponse of the coupled CO

cycle – CH

cycle – climate sys- tem.

Friedlingstein et al. (2003) expressed mathematically the magnitude of the climate-carbon cycle feedback using a gain formalism following Hansen et al. (1984). Here, we revisit this theoretical framework, first applying it to the climate- CH

gain in the absence of CO

perturbation; then generaliz- ing it to the climate, CO

and CH

interactions. These gains and the interaction between the feedbacks are expressed as functions of sensitivity terms that we estimate from the val- ues reported in the literature and from simulations performed with the ORCHIDEE global terrestrial carbon cycle model.

Once these terms are estimated, we quantify the different gains and the increase of atmospheric CH

and CO

due to the feedbacks and their interactions.

2 Theoretical analysis

In the following, the climate-CH

emissions by wetlands feedback will be referred hereafter as “C-CH

feedback” as well as “C-CO

feedback” for climate-carbon cycle feedback (both terrestrial and oceanic) in the sense of Friedlingstein et al. (2006).

2.1 C-CH

feedback analysis

Similarly to the C-CO

feedback analysis by Friedlingstein et al. (2003), we assume that the coupling between CH

emis- sions by wetlands and the climate system can be linearized by the following set of equations:

1CH

= F

+ F

− F

(1a)

1T = α

1CH

(2a)

where 1CH

(in GtC) is the difference of CH

concentration

in the atmosphere between a given time, t

, and the initial

state, t

, defined here as the preindustrial state estimated at

1860. 1T (in K) is the change in global air temperature due

to the change in CH

concentration. Equation (2a) can also

be considered as a linearization of the more stringent, square

root dependence between CH

radiative forcing and its con-

centration (IPCC, 2001). F

(GtC) represents the integral

over the period since t

of the anthropogenic emissions of

CH

. F

(GtC) represents the integral of the change in

natural CH

emissions relative to the preindustrial emissions

baseline. As the focus of this study is on wetlands, we as-

sume here that F

represents the change in CH

emissions

by wetlands only. Even though other natural sources (such

as biomass burning) are also climate dependent, and the gen-

eral framework presented here applies to other CH

sources

and sinks as well, we will focus only on the wetland compo-

nent as assessment of climate-CH

feedbacks from all natural

sources and sinks is beyond the scope of this paper.

The last term of Eq. (1a), F

(GtC), is the integral of the atmospheric sink of CH

through reaction with OH rad- icals (again relative to the preindustrial baseline) and closes the CH

budget. For the pre-industrial state, we assume here that CH

concentration was constant (apart from interannual to decadal variations), and hence natural sources were bal- anced by the atmospheric OH sink (and the minor soil sink neglected in Eq. 1a). Departure from that steady-state equi- librium can be represented by Eq. (1a), using a perturbation approach, accounting only for additional sources and sinks.

The change in CH

emissions, integrated over time t

–t

, can be driven by a change in climate and by a change in CH

con- centration. As in Friedlingstein et al. (2003), we use a single global 1T as a proxy for climate change. It is clear that a change in emissions could be also driven by changes in hy- drology, and that regional variations in both the magnitude of 1T and hydrology will also occur, but we assume here that these other climate variables change would scale with global temperature.

The integral of additional natural sources of CH

is then expressed by:

F

= β

1CH

+ γ

1T (3a) where β

(unitless) and γ

(in GtC K

) are the CH

flux sensitivities to the atmospheric CH

concentration and to cli- mate, respectively. The β

term results from the CH

atmo- spheric concentration affecting the CH

flux through its con- trol on diffusion (via soil air or plants) from wetland soils to the atmosphere. The Eq. (3a) is constructed by analogy with that for CO

given by Friedlingstein et al. (2006, Eq. 7a).

Even if the effect of increased atmospheric CH

concentra- tion on concentration gradient between soil and atmosphere (and thus the value of β

) is presumed small (atmospheric concentration in CH

∼ 1 % of wetland soil concentration), we keep it to be consistent with CO

. Although there is ev- idence that, at the site scale and on sub-annual timescales, an exponential dependence of CH

flux to temperature is ob- served (e.g. Christensen et al., 2003), Eq. (3a) here aims to represent the overall global response of wetlands to climate (not just temperature). To remain simple and comparable to the CO

framework, we thus assume that a linear relation- ship is appropriate. More investigations concerning (i) the relationship between global climate and global wetland CH

emissions and (ii) the range of temperature over which such a relationship may be valid are required. These investigations would be based, for instance, on long-term or interannual time scales.

Finally, the integral of the additional atmospheric sinks can be expressed by:

F

=

t1

Z

t0

1CH

(t )

τ dt (4a)

as the additional sink at each time step is assumed here to be equal to

, where τ is the atmospheric lifetime of

CH

. We assume here that τ is constant in time. There is a slight dependency of τ on CH

concentration and on cli- mate (IPCC, 1994) which is neglected here. In doing so, we de facto assume that there is neither year-to-year variability nor any trend in atmospheric OH concentration. Recent find- ings seem to indicate that global OH is quite stable (Montzka et al., 2011). In order to solve the set of Eqs. (1a) to (3a), one must linearize the sink term. Here by applying the mean value theorem, the integral of the changes of CH

sink over time (between the time t

and preindustrial period t

) can be written as proportional to the change of CH

at time t

. F

= µ 1CH

τ (t

− t

) (4b)

with µ considered here as a constant for a given scenario of CH

increase. For instance, µ would be equal to 0.5 if CH

concentration increases linearly with time. For a given scenario of atmospheric CH

increase, µ can be diagnosed as the ratio of the cumulative changes of CH

along the full length of the scenario to the change of CH

at the end of the scenario (equating the right members of Eqs. 4a and b).

Equation (1a) now reads:

1CH

= F

+ β

1CH

+ γ

1T − µ 1CH

τ 1t (1b) We can now express the amplitude of the feedback using a

“gain” as Friedlingstein et al. (2003) did for CO

. Combining Eqs. (2a) and (1b) we have:

1CH

= 1

1 − g

1CH

(5)

with

1CH

= F

1 +

τ

1t − β

(6)

and

g

= α

γ

. 1 + µ

τ 1t − β

(7a) 1CH

is the change of atmospheric CH

concentration in the case of C-CH

feedback while 1CH

is the change of atmospheric CH

concentration in the absence of C-CH

feedback (i.e. γ

= 0). g

is the gain of this feedback and it is larger if: α

and γ

are positive and large and if β

is positive and low. This is analogous to the C-CO

feedback gain defined in Friedlingstein et al. (2003) as:

g

= − α

γ

(1 + β

) (7b)

2.2 Cross feedbacks

The previous feedback analysis was done for the case of a changing CH

concentration alone, together with climate.

Here we extend the gain formalism in the more realistic case

where both CO

and CH

vary at the same time.

Fig. 1. Schematic representation of the C-CO₂

feedback (light grey), the C-CH

feedback (black) and of their interaction. Gas concentration effects on the soil/atmosphere fluxes are represented by dashed lines. The different sensitivity terms (α,

) are listed on this schematic representation.

First, as mentioned before, both CO

and CH

will affect the climate through their radiative forcing. 1T should be now expressed as:

1T = α

1CO

+ α

1CH

. (2b) As a consequence, F

is affected by the change in climate (Eq. 3a) regardless of whether this climate change is induced by an increase in atmospheric CH

(as showed before) or by an increase in atmospheric CO

. The same applies to a climate-induced change in land CO

sinks. Interactions re- sulting from the Eq. (2b) will be referred to as the “climate interaction” below.

The second interaction comes from the dependence of CH

emissions to atmospheric CO

. Increasing atmospheric CO

is believed to enhance plant photosynthesis (fertiliza- tion effect) (e.g. Norby et al., 2005). As a result, rising CO

should increase the amount of available organic substrate for methanogenesis and hence CH

emissions from wetlands (see discussion). This effect is expressed by an additional term (β

) in the original Eq. (3a):

F

= β

1CH

+ γ

1T + β

1CO

. (3b) This interaction will be called the “fertilization interaction”

hereafter.

The different sensitivity terms (α, β, γ) are listed on a schematic representation of the feedbacks and of their inter- action in Fig. 1.

Other minor interactions could be expressed between CO

and CH

(e.g. oxidation of CH

in atmosphere [EMA08] or

in the oxic part of wetland soils releases CO

) but these are not accounted for in our modelling approach below and are not quantified here.

One can introduce Eq. (2b) into Eq. (3b) then combine the resulting expression with Eq. (4b) into Eq. (1a) to obtain the following Eq. (8). Then, doing the same work for CO

(see Appendix A), we can obtain a two equations system with 2 unknowns (1CO

and 1CH

), i.e.

−(βC→M+γMαC)1CO2+ 1+^µ

τ1t−βM−γMα_M

1CH4=FMF (8) (1+β_C+γ_Cα_C)1CO2+γ_Cα_M1CH4=F_CF (9)

Using this system, we can express 1CO

(and 1CH

) as a function of the integral of anthropogenic CO

and CH

emissions, i.e. respectively F

and F

(or 1CO

and 1CH

; using Eq. (6) and its equivalent for CO

). We show in the following the CH

and CO

gains for the idealized (and simpler) case where β

is null (i.e. no fertilization interaction). This allows keeping symmetry between CO

and CH

. The more realistic case, accounting for this β

term and the introduced asymmetry is given in Appendix B.

Although not shown until the Appendix, this term was taken into account in all the calculations of the next sections.

For the coupled climate-CO

-CH

system neglecting fer- tilization interaction, we obtain now:

1CH

= 1 1 −

h

g

+

1−g_C

i 1CH

(10)

+ 1

1 − h

g

+

1−g_C

i α

α

g

1 − g

1CO

and

1CO

= 1 1 − h

g

+

1−gM

i 1CO

(11)

+ 1

1 − h

g

+

1−gM

i α

α

g

1 − g

1CH

Equation (10) shows that the interaction between CO

and CH

results in an additional gain in the first term of the right hand side of the equation. For CH

, this additional gain is g

g

/(1 − g

) and is in addition to the initial gain con- sidering CH

alone, g

. It represents the overall contribu- tion on the CH

concentration of the positive climate-CO

feedback initiated by the original emission-induced change in CH

concentration (climate interactions loop) in the case of no CO

anthropogenic emissions, i.e. when 1CO

= 0.

If we then account for anthropogenic CO

emissions, an additional contribution to 1CH

appears: the second term in the right hand side of the Eq. (10). This originates from the anthropogenic emissions of CO

, which induces an increase in the CO

concentration (1CO

). This CO

increase in- duces a climate change that will affect CH

emissions and hence CH

concentrations. In Eq. (10), 1CO

is multi- plied by

M

gM

1−g_C

to obtain its equivalent in 1CH

. Finally, it is multiplied by the same net feedback factor as one in the front of 1CH

. Anthropogenic emissions of CO

are independent of CH

and thus cannot be expressed as a func- tion of 1CH

. This prevents us from fully expressing the total additional gain of each feedback in the case of coupling between CO

, CH

and climate. Obviously, the same inter- pretation can be done to C-CO

feedback in presence of CH

with Eq. (11).

Changes in CO

and CH

can hence be computed from Eqs. (10) and (11), once the different sensitivity terms (α, β, γ ) are estimated. This is the aim of the next section.

3 Estimates of the gain components

In this section, we will first use simulations performed with ORCHIDEE, a dynamic global vegetation model (DGVM), to estimate the wetland emission sensitivity terms (β

, β

and γ

) as well as terms relative to C-CO

cycle. We will also make use of previous estimate of future changes in CH

emissions taken from the available literature. This will allow us to estimate the range of the climate-CH

gain and its effect on the projection of atmospheric CH

, CO

and global temperature (Sect. 4).

3.1 Based on an ORCHIDEE modelling approach 3.1.1 Wetland CH

emissions modelling into

ORCHIDEE

ORCHIDEE simulates the land energy, hydrology and the carbon cycle (Krinner et al., 2005). The version used here was further developed to incorporate CH

emissions from wetlands. The computation of wetlands CH

emissions is based on the modelling of wetland area dynamics as well as one of the CH

flux by surface unit. The resulting model will be named ORCHIDEE-WET hereafter.

In ORCHIDEE-WET, wetland area dynamics were com- puted using the TOPMODEL (Beven and Kirkby, 1979) ap- proach of Decharme et al. (2006). For each gridcell, us- ing both topographic heterogeneities and soil moisture com- puted by ORCHIDEE-WET, the TOPMODEL subroutine computes a sub-grid saturated fraction. Saturated areas as simulated by ORCHIDEE-WET do not correspond necessar- ily to water-logged soil and emitting wetland areas. Thus, we used a climatology (1993–2000) constructed from the Pri- gent et al. (2007) dataset as a baseline for our present day es- timate. Future simulated wetland extent was then calculated from the ORCHIDEE-WET simulations, corrected to sub- tract the systematic biases between the present day simulated saturated area and observed wetland distributions. More de- tails will be found in Appendix C.

At each time step, CH

flux densities (per unit area of emitting surface) were computed using a process-based model (Walter et al., 2001) for each sub-grid water-table class calculated as above. The model simulates CH

flux from natural wetlands based on the calculation of: (a) the methanogenesis in the saturated deeper soil horizons; (b) the methanotrophic oxidation in the aerated upper soil; and (c) the upward transport by diffusion, ebullition and/or plant- mediated transport (Walter and Heimann, 2000). When in- cluding the Walter et al. (2001) CH

emission model in OR- CHIDEE, we made the same following modification, de- scribed in Ringeval et al. (2010). The substrate for methano- genesis is computed from the active soil organic carbon pool computed by ORCHIDEE rather than using linear regression against soil temperature and Net Primary Productivity (NPP) as is done in Walter et al. (2001) based on 6 sites. More infor- mation can be found in Appendix D. As in the initial Walter et al. (2001) model, methanogenesis sensitivity to tempera- ture for each grid-cell is expressed by a function g as fol- lowed:

g = f (T (t, z)) · Q

(12)

where T (t, z) is the soil temperature at time t and depth z and

f (T ) is a step-function equal to 0 if temperature is negative

and 1 otherwise. A Q

of 3, close to the mean value found

in Ringeval et al. (2010), was used for all wetlands. As there

is a high uncertainty about the value of Q

(e.g. Valentine

et al., 1994), a sensitivity test with a Q

of 5.5 (in rough

agreement with higher value of range used by GCH04) is also performed. Relative to Walter and Heimann, “the tem- perature function describes the response to the seasonal vari- ation of the soil temperature [...] relative to the annual mean temperature T

at the site”. As it is not clear if T

evolves in time or not, we have tested both configurations.

Such a changing T

in time corresponds to the hypothesis that micro-organisms adapt relatively quickly to their envi- ronment (see Discussion).

The computation of a carbon stock whose active pool is used as a proxy for methanogenesis substrate is explained in a detailed way in Krinner et al. (2005). Briefly, in OR- CHIDEE, the parameterizations of litter decomposition and soil carbon dynamics essentially follow Parton et al. (1988).

Carbon dynamics are described through the exchanges of carbon between the atmosphere and the different carbon pools in plants and soils. Metabolic activity in the soil results in carbon fluxes within the three carbon pools (active, slow, and passive). Optimal residence times are prescribed for each pool, with temperature and moisture inhibition multipliers in order to parameterize the decrease of soil metabolic activity under cold or dry conditions. No modification is brought to ORCHIDEE-WET as regards soil wetlands conditions (see discussion below).

For each sub-grid water-table class given by TOPMODEL, ORCHIDEE-WET computes CH

fluxes with the corre- sponding mean water table depth value (respectively 0 and

− 5 cm). Other water table ranges could be calculated as well but would increase the time for calculation of the simula- tion. In the model, oxidation happens only in the second case, i.e. in the oxic soil layer between −5 cm and 0 for soils where the water table is 5 cm below the surface. The Q

for methanotrophy is kept equal to the initial value (= 2) of Walter et al. (2001). The model accounts also for oxidation when CH

entering the roots of plants has to pass through the small oxic zone around the root tips. A value of 50 % of the methane entering in the plant is considered as oxidized in the model (see Eq. 16 of Walter and Heimann, 2000). The CH

flux due to plant-mediated transport is a function of the Leaf Area Index (LAI) computed in ORCHIDEE-WET. As in the Walter et al. (2001) model, computation of a CH

flux which reaches the atmosphere by diffusive transport is based on the Crank-Nicolson scheme to resolve Fick’s first law. CH

at- mospheric concentration serves as the upper boundary con- dition. Ebullition and transport by plant are not functions of the CH

atmospheric concentration in the model.

Under current climate forcing (the monthly NCEP climate forcing data corrected by CRU – N. Viovy, personal com- munication, 2009, http://dods.extra.cea.fr/data/p529viov/

cruncep/readme.htm), ORCHIDEE-WET simulates a global mean wetland CH

emission flux of ∼ 251 Tg yr

over the 1990–2000 period. This is slightly above the upper end of IPCC range of estimates (100 to 231 TgC yr

) (IPCC, 2007). Both (i) the spatial extrapolation of parameter rela- tive to CH

flux densities optimized on 3 sites and (ii) the

Fig. 2. Year-to-year variability of simulated CH₄

wetlands emis- sions (grey curve) and comparison with a top-down approach (Bousquet et al., 2006) (black curve) over 1990–2002 period. The anomalies obtained by 12 months-shift mean are divided by the global annual average of each estimation (Bousquet et al., 2006 or ORCHIDEE-WET).

mismatch between mean real annual wetland extent and mean annual Prigent et al. (2007) data can lead to high simu- lated wetland emissions. The distribution over latitude bands is 68, 53 and 125 Tg yr

for boreal (>50

N), temperate (20

N–50

N) and tropical wetlands (30

S–20

N), respec- tively. High uncertainty remains for both total wetland emis- sions and their distribution. Wetland CH

emissions diag- nosed from one atmospheric inversion Bousquet et al. (2006) give an estimation of 155 Tg at the global scale over the same period with a distribution of: 32, 21 and 95 Tg for the same latitude bands as above. Comparison of the year-to-year variability of wetland CH

emissions given by ORCHIDEE- WET and Bousquet et al. (2006) is shown on Fig. 2.

This modelling approach will allow us to estimate the wet-

lands CH

emissions sensitivities to climate and to atmo-

spheric CO

and CH

concentrations for a transient run over

the period 1860–2100. Some hydrological processes such

as floodplain storage of water (Decharme et al., 2008) are

not included in the model. Concerning the representation of

permafrost, we account here for the freeze of the soil wa-

ter content and decrease in soil carbon decomposition and

soil water holding capacity under these conditions but not for high carbon content in deep soil horizons which could be decomposed under warming, nor for the possible effects of thermokarst on lake and wetland expansion.

3.1.2 Experimental design

We forced the ORCHIDEE-WET model with climate fields taken from coupled ocean-atmosphere general circulation model (OAGCM) simulations and with the associated time- varying atmospheric CO

and CH

concentrations scenar- ios. This allows us to estimate the different sensitivity terms of Eqs. (10) and (11) (or equations in Appendix B in the most general feedback calculation framework). Four ORCHIDEE-WET simulations have been performed over the period 1860–2100. Each ORCHIDEE-WET simulation needs as forcing: climate, atmospheric CO

and CH

con- centration values. For each forcing, we use either the pre- industrial state or a transient evolution from 1860 to 2100 following SRES-A2 scenario. The four ORCHIDEE-WET simulations are varied from one to the next by combining pre-industrial or transient forcing values as summarized in Table 1. This experimental design does not allow the testing of each term independently, nor their interaction effects, but is chosen to keep computational costs reasonable. Simula- tions 1 and 3 are also realized with a Q

of 5.5 for methano- genesis to test the sensitivity of our results to this parameter.

They will be called respectively Simulation 1-Q

and Sim- ulation 3-Q

in the following. We performed all these simu- lations twice: first, considering a constant T

(see Eq. 12) and second, considering a T

varying in time.

The transient climate (1860–2100) is obtained from the IPSL-CM4 OAGCM simulations (Marti et al., 2010) with prescribed GHG-forcing for historical and future (SRES A2) scenarios.. These climate fields were bias corrected by re- moving the difference between the climate model climatol- ogy (over the period 1961–1990) and the “observed” clima- tology (Sheffield et al., 2006 forcing data for air humidity and CRU – University of East Anglia’s Climate Resarch Unit, http://www.cru.uea.ac.uk/ – for all other variables). For the pre-industrial climate forcing, we use a random succession of climate data taken from the first ten years (1860–1869) of the OAGCM simulation. The same climate data succession was used for all simulations with preindustrial climate forc- ing. Before the different simulations, ORCHIDEE-WET was first brought to equilibrium using preindustrial climate forc- ing. The simulation forced by pre-industrial climate, CO

and CH

concentration can be considered as the control sim- ulation (CTRL hereafter).

By calculating the difference of the CH

emissions be- tween the different simulations, we can isolate the CH

flux sensitivities to atmospheric CO

, CH

and climate. The same is done with the net terrestrial CO

flux in order to get the carbon sensitivity terms. The difference between simula- tion 1 (change in atmospheric CO

only) and CTRL gives

Table 1.

Set of ORCHIDEE-WET simulations. Performed ORCHIDEE-WET simulations are defined by climate, atmospheric CO

and CH

concentration values used as forcing. For each forc- ing, pre-industrial values (PI) or transient following SRES-A2 sce- nario (T) can be used.

CO

CH

Climate

CTRL PI PI PI

Simulation 1 T PI PI

Simulation 2 PI T PI

Simulation 3 T PI T

PI: Pre-industrial; T: Transient over 1860–2100

the sensitivity of CO

and wetland CH

emissions to atmo- spheric CO

(resp. β

and β

). The difference between simulation 2 (change in atmospheric CH

only) and CTRL gives the wetland CH

flux sensitivity to atmospheric CH

(β

); and the difference between simulation 3 (change in CO

and climate) and simulation 1 gives the sensitivities of CO

and wetland CH

flux to climate (γ

and γ

).

Furthermore, we also estimated the contribution of changes in wetland extent vs. changes in CH

emission rate.

To do so, we remove a posteriori, the evolution of the wet- land extent from the previous estimates. For each simulation and each year, the CH

flux densities calculated per unit wet- land area are combined with the climatological pre-industrial (but seasonally varying) wetland area to compute the wet- land CH

emissions in the absence of changes to the wetland extent. Comparison as described above of such emissions gives an estimate of β

and γ

, respectively the wetland CH

flux sensitivity to atmospheric CO

and to climate under constant wetland area. Regardless, using CH

flux densities and wetland area from two different simulations to compute wetland CH

emissions does not allow the possibility of re- moving the indirect effects of the variation of wetland extent on CH

fluxes: indeed, change in simulated wetland extent leads to change in the computed soil water content (through change in modelled runoff) that could have a small effect on the ORCHIDEE modelled carbon cycle.

Finally, the difference between Simulation 1-Q

and 3- Q

, after removing wetland area evolution, gives us the wet- land CH

flux densities sensitivity to global climate with a higher Q

, i.e. the sensitivity term γ

-

.

The different γ

terms were computed for two cases: first,

from simulations performed considering a constant T

and

second, from simulations considering a T

that varies with

climate. In the case where a constant T

is chosen, mean

climatological pre-industrial surface temperature is used. If

T

varies in time, it is computed in ORCHIDEE-WET by

a slow relaxation method, as described by the Eq. (5) of Krin-

ner et al. (2005) with a τ = 365 days.

Fig. 3. Mean annual CH₄

emissions by wetlands over 2090–2099 period for CTRL simulation (a) and changes in emissions due to increase in atmospheric CO

with

= 3, constant in time

and accounting for wetland extents variation, which is the basic configuration. Climate effect on CH

flux densities alone (i.e. without accounting for wetland extent evolution, see above) is given in (e). (f) displays the change in CH

flux densities due to climate but obtained with a

variable in time.

3.1.3 Response of ORCHIDEE wetlands CH

emissions to CO

, CH

and climate

Figure 3a–d shows the mean annual CH

emissions by wet- lands for the CTRL simulation over the period 2090–2099 (Fig. 3a) as well as the changes in emissions (2090–2099 average relative to the control) due to the change in atmo- spheric CO

(Fig. 3b), climate (Fig. 3c) and both atmospheric CO

and climate (Fig. 3d). Changes in CH

emissions due to an increase in atmospheric CH

are negligible (not shown).

The changes in emissions shown in Fig. 3a–d are obtained by ORCHIDEE-WET simulations considering a methanogene- sis Q

of 3, a time-constant T

and accounting for varia- tion in wetland extent, which is considered below as the ba- sic configuration. The climate effect on CH

flux densities alone (i.e. without accounting for wetland extent evolution, as above) is given in Fig. 3e. Figure 3f displays the change in

CH

flux densities due to climate, as in Fig. 3e, but obtained with a time-varying T

.

The global averaged pre-industrial wetland CH

emis- sion amounts to 253 TgC yr

which is, as for present-day, slightly higher than previous estimates (e.g. Chappellaz et al., 1993). Changes in CH

emissions due to the various forcing show a large spatial variability. The overall effect of CO

and climate (Fig. 3d) is an increase in high latitudes, in the north- ern half of the Amazon basin, in South-east Asia and in some parts of central Africa. Elsewhere, the emissions decrease under future climate and CO

. This pattern is a combination of a widespread increase due to CO

alone (Fig. 3b) and of a general decrease due to climate change alone (Fig. 3c).

The atmospheric CO

concentration and the climate af-

fect CH

wetland emissions via two main pathways: one

due to changes in wetland areas (resulting from changes in

the soil water balance); and one due to changes in CH

flux

per unit of wetland area (resulting from changes in methano- genesis rate, in the contribution of each sort of transport, etc.). Production of CH

can be affected by changes in the temperature-dependant methanogenesis rate but also by changes in substrate quantity.

Removing the wetland extent evolution leads to reduc- ing the increase of CH

emissions under elevated CO

(not shown). The mechanism underlying this is that elevated CO

reduces the transpiration of plants, and therefore leads to an increase in soil water content given by ORCHIDEE-WET and thus an increase in the wetlands CH

emissions via an increase of the wetland areas. Wetland CH

flux densities also increase with atmospheric CO

increases. As men- tioned before, this response can be explained by the fertil- ization effect. Increased atmospheric CO

stimulates plant productivity, which leads to a rise in the active soil carbon pool and hence to more substrate available for methanogene- sis. The effect of CO

fertilization increasing productivity in ORCHIDEE-WET is similar to one of the four other DGVM models analyzed by Sitch et al. (2008).

Except for the north of South-America, the north and the north-east of Siberia, the west of China as well as the west of Canada the effect of climate change is to reduce CH

emis- sions (Fig. 3c). Removing the wetland area’s sensitivity to climate decreases largely the reduction in CH

emissions (Fig. 3e). The region of the Amazon river is an exception as climate change leads to an extension in wetlands area.

In high latitudes, the emission decrease is primarily driven by a decrease of wetland extension. In spite of extension of the active season and thus of the inundated period in this regions, the climate change would lead to a decrease in the maximum of inundated area that coincides with the period of maximum CH

flux density. In some places, the increase in methanogenesis rate, through its temperature dependence seems counterbalanced by a decrease in methanogenesis sub- strate.

Considering a T

that changes with climate over time restricts to high latitudes the places where we find an increase of CH

flux density due to climate (Fig. 3f). A varying T

reduces the CH

flux density sensitivity to temperature rep- resented by Q

formulation (Eq. 12; last term of right mem- ber). Thus, reduction in methanogenesis substrate drives the decrease displayed below 40

N. In high latitudes regions, the increase in active soil depth (switch of f (T ) from 0 to 1 for some soil layers) counterbalance the evolution of carbon soil and explain the obtained increase in CH

flux densities (Eq. 12; first term of right member).

From these simulations, we can now calculate the CO

and CH

flux sensitivity terms of Eqs. (7a) and (7b) in order to estimate the climate-CH

-CO

gains (Fig. 4). The Fig. 4a–e displays the integral of changes over 1860–2100 for CO

up- take and wetland CH

emissions as function of atmospheric CO

(Fig. 4a–b), atmospheric CH

(Fig. 4c) and climate (Fig. 4d–e) and the slopes of these different curves give the sensitivity terms’ values. The results shown in Fig. 4 shows

a linear relation between additional CH

and CO

flux and atmospheric CH

, atmospheric CO

, or climate over the pe- riod modeled here is supported by the model. This supports the assumption of a first-order linear relation in the theoret- ical analysis of Sect. 2. The ORCHIDEE-WET computed sensitivity values in 2100 are summarized in the Table 2 in the same units for CO

and CH

. We note that the global net terrestrial CO

flux sensitivity to rising atmospheric CO

(β

) and to climate change (γ

), depend also on the ocean carbon response. We used ocean sensitivity terms (β

and γ

) from Friedlingstein et al. (2006) for the IPSL coupled- climate-carbon model to account for the ocean CO

uptake feedbacks. Thus, β

(respectively γ

) in the Table 2 is the sum of the land flux sensitivity β

(resp. γ

) computed using Fig. 4a (resp. Fig. 4d) and of the ocean flux sensitivity β

(resp. γ

).

The individual sensitivity of the land CO

flux to atmo- spheric CO

(Fig. 4a) as well as its response to global warm- ing (Fig. 4d) is not discussed here. A comprehensive analysis can be found in Friedlingstein et al. (2003).

Concerning CH

emissions from wetlands, as mentioned above, we obtain an increase of emissions when atmo- spheric CO

increases (Fig. 4b). β

amounts to 0.0142 by 2100. ORCHIDEE-WET simulates a negative effect of atmospheric CH

on wetland CH

emissions, β

(Fig. 4c).

The increase in atmospheric CH

leads to a decrease in the concentration gradient between wetland soil and the atmo- sphere, which drives a decline in the diffusive flux of CH

from soil, and thus a larger proportion of the CH

created is consumed by methanotrophy within the soils. However, the negative value of the sensitivity of emissions to atmospheric CH

is very low (β

= −0.0040) as assumed before and is explained by the fact that the CH

atmospheric concentra- tions always remains much lower than the CH

concentration in wetland soils.

As mentioned before (Fig. 3c), the simulated overall effect of climate changes is to reduce CH

emissions from wetlands (Fig. 4e). We find a sensitivity γ

of − 1.83 GtC K

. As- suming constant wetland area would change the sign of the sensitivity term, with a γ

of +1.27 GtC K

. Hence, the overall climate-driven decline in CH

emission from wet- lands is mainly driven by a decrease in wetland area. The negative value of γ

obtained in the case where we con- sider a varying T

and do not include the dynamics of wetland area changes (γ

= − 0.84 GtC K

) shows that a re- duction of the methanogenesis substrate reinforces the nega- tive effect of climate on emissions driven by wetland extent.

If a constant T

is used, taking a higher methanogenesis Q

value (Q

= 5.5) leads to few changes when account- ing for wetland extent (+17 %; from − 1.83 to − 1.51) but a large change when not accounting for (more than 3 times;

form +1.27 to +5.37).

Fig. 4. (a)–(e): Evolution of the integral of change in CO₂

land uptake and CH

wetlands emissions as function to atmospheric CO

concentration – (a) and (b), atmospheric CH

concentration (c) and global air temperature (e). Be careful for the different y-axis unit for (c).

Blue curves of (b) and (e) correspond to the evolution of the integral of change in CH

wetlands emissions after removing the wetland extent

evolution (i.e. using for all the time step the pre-industrial wetland extent). Red curve of (e) is the same as blue one but with a higher

for the methanogenesis. (f)–(g): Temperature sensitivity to atmospheric CO

and CH

.

Table 2. Values of the CO₂

and CH

flux sensitivity in 2100 (top) as well as climate one (bottom). Given global net terrestrial CO

flux sensitivities are sum of ocean sensitivity terms from Friedlingstein et al. (2006) and the estimation of land flux sensitivity based on ORCHIDEE-WET simulations (cf. Fig. 4). Wetland CH

emissions sensitivity reported in this table are only based on ORCHIDEE-WET simulations and are also consistent to each other.

Flux sensitivity in 2100

CO

flux CH

flux

to atmospheric CO

= 1.11 With dynamic wetland

= 0.0142

(unitless) Without dynamic wetland

= 0.0155

to atmospheric CH

=

0.0040

(unitless)

to climate

=−82.3 Constant Variable

(in GtC K

)

Q₁₀

= 3 With dynamic wetland

=−1.83

=

= 3 Without dynamic wetland

= +1.27

=

0.84

= 5.5 With dynamic wetland

=

1.51

=

4.85

= 5.5 Without dynamic wetland

= +5.37

=

Climate sensitivity

to atmospheric CO

= 0.0029

(in K GtC

)

to atmospheric CH

= 0.0840

(in K GtC

)

When T

varies in time, changing the Q

tends to in- crease γ

in high latitudes (not shown) due to the activation of some soil layers. At the global scale, this effect is hid- den by small changes in contribution of the different latitudes bands to the total emissions from simulation with Q

= 3 to simulation with Q

= 5.5 (not shown).

3.2 Literature based estimates of β

and γ

As mentioned before and despite some remaining uncertainty (e.g. because of interaction with nitrogen cycle), the CO

flux sensitivities to climate and atmospheric CO

have been al- ready studied and estimated (notably the C

MIP intercom- parison; Friedlingstein et al., 2006). In the present study, most uncertainty concerns terms relative to the sensitivity of wetlands CH

emissions.

A pair of previous studies investigated the future changes in CH

emissions from wetlands. Although these studies did not quantify the CH

emissions sensitivity to climate and at- mospheric CO

(respectively γ

and β

) one can use their results to derive these quantities.

Neither of the previous studies (SWF04, GCH04, EMA08 and V08) explicitly accounted for changes in CH

concen- tration and its effect on CH

. To our knowledge there are also no site-level manipulative experiments with increased CH

concentration conditions. Therefore we cannot provide

a literature based estimate of β

. However, we found this term to be negligible (see previous section).

A first-order estimate of γ

is possible from SWF04, GCH04 and EMA08. Their approach does not account for the fertilizing effect of high CO

atmospheric level on wet- land CH

emissions but only for the effect of the climate change induced by it. Thus, they allow for a direct esti- mate of γ

. SWF04 estimate a rise of 78 % of wetlands CH

emissions (from 156 to 277 Tg yr

) under a transient 2 × CO

climate with a global warming of 3.4

C. The cal- culation of γ

needs the time evolution of the wetland CH

emission, as it is the ratio of the cumulated emissions divided by the related warming. Not having this time evolution, we assume here that the growth of CH

emission is linear, as the warming is close to linear in such transient 2 × CO

climate simulations (e.g. Cubasch et al., 2001). This gives a value of 0.93 GtC K

for γ

. The same estimate of γ

can be done with GCH04 where they simulate a wetland CH

emis- sion increase of 255 Tg yr

over 110 years for a warming of 4.2 K (in their reference case, CTRL). This gives a value of 2.70 GtC K

for γ

.

EMA08 find an increase of 130–140 to 170–200 Tg yr

under the SRES-A2 scenario (+3.4

K) but the accounted ef-

fects of climate warming on wetland CH

emissions are only

relative to temperature dependency of methanogenesis and

to change in soil depth when permafrost thaws. Both wet-

land extent and water table depth are constant during their

simulation time and the methanogenesis substrate is con- stant. Such an increase gives a γ

value of ∼1.9 GtC K

.

V08 obtained a wetland CH

emissions increase of +40 % from 20th to the end of 21st century (from 240 Tg yr

to 340 Tg yr

) under a warming of 3.5

C (scenario A1B). The results cannot be easily delineated into the theoretical frame- work we have developed in this paper: CO

fertilization ef- fect on wetland CH

emissions seems to be accounted for (the paper uses NPP to approximate substrate) but is not dis- cussed. Thus we cannot estimate the γ

and β

effects based on this study.

We also note that the evolution of the global temperature in these previous studies is not the same as one simulated by the ISPL-CM4 OAGCM under SRES-A2. It has been shown for the C-CO

feedback that the rate of perturbation has an impact on the estimate of γ

(Gregory et al., 2009). The same certainly applies for the C-CH

feedback and the value of γ

considered here.

Finally, wetland CH

emissions sensitivity to temperature derived through warming manipulation on sites (e.g. Upde- graff et al., 2001; White et al., 2008) could not be used to estimate γ

because this term represents the overall global response of wetlands to climate and not just to temperature.

The published global modeling approaches do not give an estimate of the relationship between atmospheric CO

level and global wetlands CH

emissions. However, there are wet- lands site level manipulative experiment where emissions are measured under ambient and elevated CO

(e.g. Dacey et al., 1994; Megonigal and Schlesinger, 1997; Kang et al., 2001;

Vann and Megonigal, 2003; Pancotto et al., 2010). The mea- sured response varies between 0 % (Pancotto et al., 2010) and 136 % under 2 × CO

(Megonigal and Schlesinger, 1997) according to the wetland type and the experimental condi- tions. ORCHIDEE-WET simulated wetland CH

emissions increase by +80 % (respectively ∼ +50 % with no evolution of wetland extent) when atmospheric CO

concentration given by SRES-A2 scenario grows from 355 to 716 ppm. The speed of the CO

perturbation of the manipulations experi- ment is totally different from that under the SRES-A2 sce- nario. Moreover, the relationship between atmospheric CO

concentration and wetland CH

emissions estimated at sites is extrapolated to global scale with difficulty. Thus we retain only the ORCHIDEE-WET based β

in the following. In Sect. 4, the effect of the different interactions on atmospheric CH

and CO

will be added successively. The effect without CO

fertilization on CH

emissions could be seen as lowest boundary of the uncertainty range for accounting for β

. In summary, we find an estimate for β

, based on ORCHIDEE-WET, of − 0.0040 and for β

of 0.0142. For γ

, we find, based on both ORCHIDEE-WET and literature based estimates, a range from − 1.83 to +2.70. The value of γ

chosen as representative of ORCHIDEE-WET simu- lation corresponds to the best estimate (i.e. accounting for variation in wetland extent, Q

= 3 and a constant T

).

ORCHIDEE-WET gives a negative value for γ

while the

estimates based on GCH04 and SWF04 give a positive γ

. An analysis on the reasons for the uncertainty on the sign of γ

will be given in the discussion section.

3.3 Other terms

In order to estimate the gains, we finally have to calculate the climate sensitivity to CO

and to CH

(α

and α

re- spectively) as well as µ, the atmospheric OH sink scaling term (Eq. 4b).

For α

, we used the transient global warming of the IPSL- CM4 model from an idealized simulation with changes in atmospheric CO

only (CMIP 1 % yr

) (Fig. 4f). This gives a α

of 0.0029 K ppm

. For α

we have no parallel climate simulation with change in CH

concentration only. Thus, we used the standard CO

radiative forcing equations (IPCC, 2001, Table 6.2) to derive a climate sensitivity to changes in radiative forcing (1RF) from the previous simulation. The same standard radiative forcing equations, but for CH

, al- low us to go from 1RF to an equivalent of atmospheric CH

concentration, if we assume the same climate sensitivity for 1RF whether it is due to CO

or CH

. We can also estimate the warming due to CH

only (Fig. 4f). This gives a α

of 0.0840 K ppm

.

We compute µ, the atmospheric OH sink scaling term, as the ratio of the cumulative changes of atmospheric CH

along the SRES-A2 scenario to its change at the end of the scenario. We find a µ of 0.322. Anthropogenic emis- sions of CH

, F

, come from the EDGAR database (http://

www.sec.gov/edgar.shtml) for the historical period and from the SRES-A2 scenario for the 21st century. The CH

at- mospheric lifetime, τ , is assumed constant with a value of 9 years (IPCC, 2001). This lifetime is sensitive to the atmo- spheric composition (e.g. COV, see Valdes et al., 2005) and in particular to CH4 concentration itself (e.g. V08), leading to a feedback. IPCC (2007) gives an adjustment time (Lelieveld et al., 1998) of 12 years to account for indirect effects of increase in CH

emissions. Not using of a coupled climate- chemistry model, we cannot account for dependency of τ on CH

concentration and on climate.

4 Estimation of the feedbacks’ gains and their interaction

4.1 C-CH

and C-CO

feedbacks’ gains

Once the sensitivity terms are estimated, we computed the gains of the C-CO

and C-CH

feedbacks when each gas is considered alone (Eqs. 7a and b), as well as the interaction between these feedbacks as defined in Eqs. (10) and (11).

Combining our range of γ

(from − 1.83 to 2.70 GtC K

;

see above) we find the C-CH

feedback gain, g

, when

CH

is considered alone, ranging between − 0.016 and 0.024

by 2100, respectively obtained for the best ORCHIDEE-

WET estimated γ

and literature estimated γ

The sign

of the gain is controlled by the γ

. Negative gains are due to the negative wetland emission sensitivity to climate found in ORCHIDEE-WET. For the C-CO

feedback gain, using our ORCHIDEE-WET simulations, we find a value of 0.113, slightly higher than the value found in Friedling- stein et al. (2006).

Going back to Eqs. (10) and (11), we can now calculate the cross-gains terms when not accounting for the fertilization interaction. For CH

concentration changes (Eq. 10), the g

gain is augmented by g

· g

/(1 − g

), the additional gain due to the interaction between CO

and CH

. Using a γ

of

− 1.83 GtC K

, this cross-gain is equal to − 0.0017 which represents a correction of ∼ 10 % of the initial gain g

. Sim- ilarly, for CO

(Eq. 11), the cross-gain term g

· g

/(1 − g

) amounts to − 0.0015 which represents only ∼ 1.5 % of g

. The CO

contribution to CH

is larger than the reciprocal because climate has a larger absolute effect on the net CO

flux than on the CH

emissions from wetlands. If we use the upper estimate of g

, the cross-gains due to the interactions between C-CO

and C-CH

feedbacks have similar effects on g

and g

(cross-gain ∼13 % of g

and ∼3 % of g

).

4.2 Effect on atmospheric CO

, CH

and global temperature

We compute the changes of CH

in the atmosphere between future (2100) and pre-industrial time, 1CH

, in the case of C-CH

feedback alone, and then with cross-feedbacks ac- counted, for using Eq. (10) (or equations from Appendix B for the most general case). 1CH

and 1CO

are expressed in the following in ppbv and ppmv, respectively. Figure 5a shows the incremental changes in the calculated 1CH

when accounting for successive gains. 1CH

is the change in CH

in the absence of any retroaction, as given by Eq. (6).

Then we account successively for the climate-CH

feedback (i.e. CH

emissions dependence on CH

induced tempera- ture change), the climate interaction as explained in Sect. 2.2 (i.e. temperature dependence to atmospheric CO

; α

6= 0) and the fertilization interaction (i.e. CH

emissions depen- dence to atmospheric CO

; β

6= 0). Figure 5b shows the same calculation, but for 1CO

. For each gas, we plotted both the case with (solid line) and without (dashed line) an- thropogenic emissions of the other gas. All calculations were done with the ORCHIDEE-WET based estimated β

. However, given the high uncertainty on γ

, we plotted also the case with the positive γ

derived from literature (in grey) or with the negative γ

based on the best ORCHIDEE-WET estimation (in green). We add also the case where T

is variable in time (in blue). As a first check on our frame- work, we compared the uncoupled estimates of 1CH

and 1CO

to the values given by the SRES-A2 scenario, where none of the feedbacks presented here were accounted for. We find a CH

concentration increase by 2100 of 3030 ppb and a CO

concentration change of 496 ppm, not far from the SRES-A2 concentration changes (2925 ppbv for CH

and

5450 ppm for CO

; IPCC, 2001). This indicates that, for CH

, the assumption of a constant lifetime and the use of the scaling parameter µ are appropriate. We note that the CO

concentrations given in IPCC (2001) already accounts for a C-CO

feedback.

Concerning CH

(Fig. 5a), accounting for the different feedbacks does not have a large effect on the calculated CH

concentration as long as anthropogenic CO

emissions are neglected (dashed lines). This is because the climate effect of CH

anthropogenic emissions alone is too weak to gen- erate a non-negligible C-CH

or C-CO

feedback. Only the CO

emissions induced climate change leads to a large effect on CH

emissions and CO

sinks and hence modify the cal- culated CH

concentration. This is clearly different for the CO

(Fig. 5b) for which its own feedback with the climate explains most of the 1CO

(at least 80 % of the 1CO

given with all interactions).

When anthropogenic CO

emissions are included, the large change in atmospheric CO

affects CH

emissions through (i) the climate effect on CH

emissions and (ii) the fertilization effect on substrate. Figure 5a shows that these two terms are important. Depending on the sign of γ

, the CO

induced climate effect will enhance (grey line) by 457 ppb or reduce (green line) by 310 ppb the calculated CH

concentration. This climate interaction includes temperature change due modification of 1CO

caused by both anthro- pogenic emissions and C-CO

feedback. The CO

fertiliza- tion effect is always positive and, depending on the previous value of γ

, further increase (red line) or compensate (blue line) the CO

induced climate effect.

When accounting for all interactions between CO

and CH

, 1CH

is 1400 ppb larger than the uncoupled 1CH

in the case of positive γ

and 475 ppb larger in the nega- tive case (with constant T

). Variable T

leads to an increase of only 190 ppb.

For CO

(Fig. 5b), as mentioned above, most of the change in the calculated concentration comes from the C-CO

gain, where 1CO

rise from 495 to 560 ppm. Accounting for the interactions with CH

slightly changes this value and can lead to an increase of 15 ppm. The climate change induced by anthropogenic CH

emissions is preponderant to the C- CO

-CH

effect on the 1CO

(comparison between dash and plain lines) while the C-CH

feedback induced climate change has only a small effect. In all the cases, the increase in wetland CH

emissions induced by the fertilization inter- action has a little effect on 1CO

(∼3 ppm).

The change in global temperature, 1T that would follow

these different changes in atmospheric CO

and CH

can be

estimated using Eq. (2b). Several combinations of 1CH

and 1CO

are possible, according to the interactions that

are accounted for. Here, we limit the 1T computation to

specific cases. In the absence of anthropogenic CH

emis-

sions, accounting for C-CO

feedbacks leads 1T to rise from

3.05 to 3.44 K. Accounting for anthropogenic CH

emissions

in addition leads 1T to rise to 3.98 K. In the case where γ